In the shortest path routing algorithm for communication networks, the end-to-end path of each session is found such that the sum of weights of links on the path is minimized. Hence, to find a `good' path for each session, it is important to assign the appropriate weight to each link in the network. In this paper, we study this problem considering the utilization of each link. Since this problem is known to be NP-hard[1], we use a heuristic approach. Our algorithm is based on the simulated annealing algorithm. However, with taking into account the properties of our problem, we modify the basic simulated annealing algorithm, which results in a faster and more robust convergence.